In this script, we share the code to replicate our parameters.
Create architecture for scripts, visuals and data. Includes
sensitivity_analysis_lq
dat_p.csv : price & quantity data from seizures
(Source: collated by the Environmental Investigation Agency (EIA) and
processed for analysis by authors).
totoaba_biomass_catch_20230516.csv : historical
biomass and catch (Source: INAPESCA 2020).
w_par.csv: cost data from for poaching costs (see
Supplementary Materials).
v_par.csv: cost data from for aquaculture costs (see
Supplementary Materials).
## `geom_smooth()` using formula = 'y ~ x'
## Saving 7 x 5 in image
## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = price_ton_toto ~ c, data = new_dat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -669851 -246794 -50249 201334 1366925
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1625837 406790 3.997 0.000248 ***
## c -1564 726 -2.154 0.036890 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 431700 on 43 degrees of freedom
## Multiple R-squared: 0.09739, Adjusted R-squared: 0.0764
## F-statistic: 4.64 on 1 and 43 DF, p-value: 0.03689
## [,1] [,2]
## [1,] "K" "M"
## [2,] "Winfinity" "Loo"
## [3,] "tmax" "tm"
## [4,] "Lm" "Temperature"
## [5,] "ln_margsd" "rho"
## [6,] "logitbound_h" "ln_r"
## Closest match: Actinopterygii_Perciformes_Sciaenidae_Totoaba_macdonaldi
| x | |
|---|---|
| Loo | 4.9184344 |
| K | -1.5830689 |
| Winfinity | 10.0590626 |
| tmax | 2.7171232 |
| tm | 1.3175891 |
| M | -1.0570853 |
| Lm | 4.1868676 |
| Temperature | 24.0087354 |
| ln_var | -2.7136658 |
| rho | 0.6039179 |
| ln_MASPS | -0.1039645 |
| ln_margsd | -1.0414289 |
| h | 0.5263985 |
| logitbound_h | -0.5141059 |
| ln_Fmsy_over_M | -0.0887666 |
| ln_Fmsy | -1.1601266 |
| ln_r | -1.9234144 |
| r | 0.2012827 |
| ln_G | 2.1021294 |
| G | 8.3517745 |
First :
Use w_parto reconstruct costs of crew earning, food,
fuel, gear
Compute a cost per trip, with confiscations of gear and vessels
Compute sub-seasonal average costs
We have average cost data, for bins of trips. Here, I estimate a cost function for all the effort levels, that maps the number of trips to their total cost, taking into account different bins.
## [1] 0 40 520 1920
## [1] 14386.69
The kinky total cost function could be best approximated with a linear term. However, to model the increasing opportunity costs of having more fishermen, it would be nice to have a quadratic term, to forecast the future.
Find the parameter \(W_{quad}\) such that : \[ TotCost(E)=WE^2 \Rightarrow MargCost(E) = 2W_{quad}E \]
And
\[ MargCost(E_{hist}) = AvgCost(E_{hist})\Rightarrow W_{quad} = \frac{W_{avg}}{2E_{hist}} \]
First, find best estimate of modeled cost in a MMSE sense.
## [1] "Optimal W1 in an MMSE sense is : 0"
## [1] "Optimal W2 in an MMSE sense is : 7193.34486399167"
Result from MMSE suggest to use the linear form, without reference to a quadratic term. However, increasing cost of effort is consistent with a disaggregated view of the fishery. Force a quadratic term.
| W1 | W2 | diff% | mse |
|---|---|---|---|
| 0 | 0.0000000 | 0.0000000 | 0 |
| 11000 | 0.8819504 | 11.7702188 | 30647515448353752 |
| 11400 | 0.7777838 | 10.3800450 | 24033220500031512 |
| 11800 | 0.6736171 | 8.9898711 | 18274620332517136 |
| 12200 | 0.5694504 | 7.5996973 | 13371714945810632 |
| 12600 | 0.4652838 | 6.2095234 | 9324504339911994 |
| 13000 | 0.3611171 | 4.8193495 | 6132988514821220 |
| 13400 | 0.2569504 | 3.4291757 | 3797167470538315 |
| 13800 | 0.1527838 | 2.0390018 | 2317041207063276 |
| 14200 | 0.0486171 | 0.6488279 | 1692609724396104 |
Here, I keep as the baseline specification the first value with low difference with cost
Export data for \(W\) and the corresponding model parameters for the quadratic model (\(W\)) and linear-quadratic model (\(W_1\) and \(W_2\))
We use c= 0 as trading costs.
At 4.5 years under farming conditions, a totoaba should have a 416.96g swim bladder. At 5 years under farming conditions, a totoaba should have a 529.78 g swim bladder
The quasi fixed cost for pens is cost_pen from the Buche
Bros data
| params | value | concept | units |
|---|---|---|---|
| alpha | 1625836.98 | Demand model : intercept | USD |
| beta | 1563.75 | Demand model : coefficient | USD/metric ton of biomass |
| r | 0.20 | Intrinsic growth rate | unitless |
| k | 20226.00 | Carrying capacity (in metric tons) | metric tons of biomass |
| sigma | 0.00 | Catchability | % of biomass/vessel trip |
| avg_cost | 14386.69 | Average cost per vessel trip at historical value | USD/vessel trip |
| W_high | 3.75 | Quadratic cost parameter - Quadratic cost function | USD vessel trip\(^{-2}\) |
| fixed_cost | 13811222.14 | Fixed cost - Quadratic cost function | USD |
| W1 | 12200.00 | Linear cost parameter - Linear quadratic cost function | USD/vessel trip |
| W2 | 0.57 | Quadratic cost parameter - Linear quadratic cost function | USD vessel trip\(^{-2}\) |
| age | 4.50 | Age of farmed totoaba | Years |
| gamma | 1354.25 | Demand model : substitutable good coefficient | USD/metric ton of biomass |
| v | 89929.92 | Unit cost of farming | USD/metric ton of biomass |
| i_r | 0.10 | Interest rate | % |
| c | 0.00 | Unit cost of trading | USD/ metric ton of biomass |
| cost_pen | 200000.00 | Cost of pen | USD |
In this section, I load data for the baseline calibration using the linear and linear quadratic cost models.
| params | value | concept | units |
|---|---|---|---|
| alpha | 1625836.98 | Demand model : intercept | USD |
| beta | 1563.75 | Demand model : coefficient | USD/metric ton of biomass |
| r | 0.20 | Intrinsic growth rate | unitless |
| k | 20226.00 | Carrying capacity (in metric tons) | metric tons of biomass |
| sigma | 0.00 | Catchability | % of biomass/vessel trip |
| avg_cost | 14386.69 | Average cost per vessel trip at historical value | USD/vessel trip |
| W_high | 3.75 | Quadratic cost parameter - Quadratic cost function | USD vessel trip\(^{-2}\) |
| fixed_cost | 13811222.14 | Fixed cost - Quadratic cost function | USD |
| W1 | 12200.00 | Linear cost parameter - Linear quadratic cost function | USD/vessel trip |
| W2 | 0.57 | Quadratic cost parameter - Linear quadratic cost function | USD vessel trip\(^{-2}\) |
| age | 4.50 | Age of farmed totoaba | Years |
| gamma | 1354.25 | Demand model : substitutable good coefficient | USD/metric ton of biomass |
| v | 89929.92 | Unit cost of farming | USD/metric ton of biomass |
| i_r | 0.10 | Interest rate | % |
| c | 0.00 | Unit cost of trading | USD/ metric ton of biomass |
| cost_pen | 200000.00 | Cost of pen | USD |
Define function where variable is either x i.e
population stock, or s i.e price paid to poachers. All the
parameters take default values specified in the global environment.
growth(x, ...) : logistic growth function, yields
growth of population (in metric tons)
monop_harvest(x, ...): harvest (in metric tons) when
trader is a monopolist
monop_harvest_lq(x, ...): harvest (in metric tons)
when trader is a monopolist and cost structure is linear
quadratic
cournot_harvest(x, ...),
bertrand_harvest(x, ...): harvest (in metric tons) when
trader and farmer compete in Cournot, i.e, set quantities
strategically, and Bertrand, i.e, set prices
strategically.
cournot_harvest_lq(x, ...) : harvest (in metric
tons) when trader and farmer compete in Cournot i.e, set
quantities strategically and cost structure is linear quadratic
price_poachers_cournot(x, ...),
price_poachers_bertrand(x, ...): price paid to poachers (in
USD/metric tons) when trader and farmer compete in Cournot and
Bertrand
price_poachers_bertrand(x, ...): price paid to
poachers (in USD/metric tons) when trader and farmer compete in
Bertrand and cost structure is linear quadratic
bertrand_harvest_lq(x,...) is set replacing the
price that clears the primary market in the harvest function of
fishermen.
cournot_farmed(s, ...),
bertrand_farmed(s, ...): quantity farmed (in metric tons)
when trader and farmer compete in Cournot and
Bertrand
Generate results saved at
~/data/outputs/results_all_models.csv :
W_lq_new: each row corresponds
to a cost parameter \(W\), \(W_1\) and \(W_2\)To understand the impact of different \(W_1\) & \(W_2\) divides :
Clearly, the choice of \(W_1\) and \(W_2\) is important with respect to the anticipated equilibrium in the vertical monopoly case : with a linear-quadratic cost function, we no longer can say the monopoly will achieve a healthy steady state population. The results in the post intervention world are robust to the cost specification, and guarantee population increases in the quantity adjustment scenario, while population may marginally diminish in the price setting scenario.
First, illustrate the new equilibria with the same \(W\) = 3.7465338 value and the prefered solution for \(W_1\) and \(W_2\) (e.g 12200, 0.57) in the linear quadratic cost of effort specification.
Save plot for final results :
Define bio-economic performance by combining population variables (stock and harvest) with price and profit data from economic model.
Change in number of totoabas :
| Scenario | Poached harvest (in mt) | Farmed harvest (in mt) | Steady state population (in mt) | Retail price (in USD/ton of buche) | Retail price of 500g buche (in USD) | Price paid to poacher (in USD/ton of buche) | Poacher price of 500g buche (in USD) | Illegal profit (in million USD) | Farming profit (in million USD) | Fishing profit (in million USD) | Aggregate profit (in million USD) | Aggregate profit change (in million USD) | Farming profit change (in million USD) | Illegal profit change (in million USD) | Fishing profit change (in million USD) | Variation in ss. pop. | Poaching change (%) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Price setting - LQ cost | 536.70 | 430.05 | 17235.0 | 204179.1 | 5247.402 | 39870.05 | 1024.6602 | 88.18 | 58.14 | 3.57 | 149.89 | -253.35 | 58.14 | -313.84 | 2.34 | -0.24% | 5.85% |
| Vertical Monopoly - LQ cost | 507.04 | 0.00 | 17277.0 | 832955.7 | 21406.962 | 40074.46 | 1029.9136 | 402.02 | 0.00 | 1.22 | 403.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0% | 0% |
| Quantity adjustment - LQ cost | 363.71 | 333.60 | 18220.5 | 605295.6 | 15556.098 | 36537.13 | 939.0044 | 206.87 | 173.43 | 0.57 | 380.86 | -22.38 | 173.43 | -195.16 | -0.66 | 5.46% | -28.27% |
| Price setting | 520.27 | 425.30 | 17184.0 | 236298.3 | 6072.866 | 32903.89 | 845.6299 | 105.82 | 70.11 | 8.56 | 184.49 | -229.80 | 70.11 | -300.33 | 0.42 | -0.43% | 2.09% |
| Vertical Monopoly | 509.64 | 0.00 | 17259.0 | 828894.3 | 21302.583 | 31951.60 | 821.1560 | 406.15 | 0.00 | 8.14 | 414.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0% | 0% |
| Quantity adjustment | 369.87 | 330.94 | 18182.0 | 599279.2 | 15401.476 | 20894.42 | 536.9866 | 213.93 | 170.66 | 3.86 | 388.45 | -25.84 | 170.66 | -192.22 | -4.28 | 5.35% | -27.42% |
New version for manuscript :
| Scenario | Poached harvest (in mt & % change) | Farmed harvest (in mt) | Steady state population (in mt & % change) | Trader profit (in million USD and change) | Fishing profit (in million USD and change) | Farming profit |
|---|---|---|---|---|---|---|
| Linear quadratic cost | ||||||
| Vertical Monopoly | 507.04 | 0 | 17277 | 402.02 | 1.22 | 0 |
| 0% | 0% | 0 | 0 | |||
| Quantity adjustment | 363.71 | 333.6 | 18220.5 | 206.87 | 0.57 | 173.43 |
| -28.27% | 5.46% | -195.16 | -0.66 | |||
| Price setting | 536.7 | 430.05 | 17235 | 88.18 | 3.57 | 58.14 |
| 5.85% | -0.24% | -313.84 | 2.34 | |||
| Quadratic cost | ||||||
| Vertical Monopoly | 509.64 | 0 | 17259 | 406.15 | 8.14 | 0 |
| 0% | 0% | 0 | 0 | |||
| Quantity adjustment | 369.87 | 330.94 | 18182 | 213.93 | 3.86 | 170.66 |
| -27.42% | 5.35% | -192.22 | -4.28 | |||
| Price setting | 520.27 | 425.3 | 17184 | 105.82 | 8.56 | 70.11 |
| 2.09% | -0.43% | -300.33 | 0.42 |
Table for manuscript :
| Scenario | Poached harvest (in mt) | Farmed harvest (in mt) | Steady state population (in mt) | Illegal profit (in million USD) | Farming profit (in million USD) | Fishing profit (in million USD) | Aggregate profit (in million USD) | Illegal profit change (in million USD) | Variation in ss. pop. | Poaching change (%) |
|---|---|---|---|---|---|---|---|---|---|---|
| Vertical Monopoly | 507.04 | 0.00 | 17277.0 | 402.02 | 0.00 | 1.22 | 403.24 | 0.00 | 0% | 0% |
| Quantity adjustment | 363.71 | 333.60 | 18220.5 | 206.87 | 173.43 | 0.57 | 380.86 | -195.16 | 5.46% | -28.27% |
| Price setting | 536.70 | 430.05 | 17235.0 | 88.18 | 58.14 | 3.57 | 149.89 | -313.84 | -0.24% | 5.85% |
Redo parameter for sensitivity analysis :
Define model run, and yield exploit_ a dataset with
parameters and corresponding steady states.
Check the occurrence of steady states :
## Saving 7 x 5 in image
| names | x | x_norm | multiplier_global |
|---|---|---|---|
| Price setting | 17235.0 | -0.2430978 | 0 % |
| Vertical monopoly | 17277.0 | 0.0000000 | 0 % |
| Quantity adjustment | 18220.5 | 5.4610175 | 0 % |
| Vertical monopoly | 1361.0 | -92.1224750 | -10 % |
| Vertical monopoly | 1598.0 | -90.7507090 | -10 % |
| Vertical monopoly | 17267.5 | -0.0549864 | -10 % |
| Price setting | 17205.5 | -0.4138450 | -10 % |
| Quantity adjustment | 18210.0 | 5.4002431 | -10 % |
| Price setting | 17261.5 | -0.0897146 | 10 % |
| Vertical monopoly | 17286.0 | 0.0520924 | 10 % |
| Quantity adjustment | 18229.0 | 5.5102159 | 10 % |
| Price setting | 17289.5 | 0.0723505 | 20 % |
| Vertical monopoly | 17295.0 | 0.1041848 | 20 % |
| Quantity adjustment | 18238.5 | 5.5652023 | 20 % |
| Vertical monopoly | 17304.5 | 0.1591712 | 30 % |
| Price setting | 17317.0 | 0.2315217 | 30 % |
| Quantity adjustment | 18248.0 | 5.6201887 | 30 % |
Need a subsidy rate of 20% to avoid poaching increase, eg need \(v=\) 71943.9322629
## Saving 7 x 5 in image
| names | x | x_norm | namer |
|---|---|---|---|
| Price setting | 17229.5 | -0.2749320 | 11000 and 0.88 |
| Vertical monopoly | 17275.5 | -0.0086821 | 11000 and 0.88 |
| Quantity adjustment | 18216.5 | 5.4378654 | 11000 and 0.88 |
| Price setting | 17231.5 | -0.2633559 | 11400 and 0.78 |
| Vertical monopoly | 17276.0 | -0.0057880 | 11400 and 0.78 |
| Quantity adjustment | 18218.0 | 5.4465474 | 11400 and 0.78 |
| Price setting | 17233.0 | -0.2546738 | 11800 and 0.67 |
| Vertical monopoly | 17276.5 | -0.0028940 | 11800 and 0.67 |
| Quantity adjustment | 18219.0 | 5.4523355 | 11800 and 0.67 |
| Price setting | 17235.0 | -0.2430978 | 12200 and 0.57 |
| Vertical monopoly | 17277.0 | 0.0000000 | 12200 and 0.57 |
| Quantity adjustment | 18220.5 | 5.4610175 | 12200 and 0.57 |
| Vertical monopoly | 1106.5 | -93.5955316 | 12600 and 0.47 |
| Vertical monopoly | 1842.5 | -89.3355328 | 12600 and 0.47 |
| Vertical monopoly | 17278.0 | 0.0057880 | 12600 and 0.47 |
| Price setting | 17236.5 | -0.2344157 | 12600 and 0.47 |
| Quantity adjustment | 18221.5 | 5.4668056 | 12600 and 0.47 |
| Vertical monopoly | 934.0 | -94.5939689 | 13000 and 0.36 |
| Vertical monopoly | 2014.5 | -88.3399896 | 13000 and 0.36 |
| Vertical monopoly | 17278.5 | 0.0086821 | 13000 and 0.36 |
| Price setting | 17238.5 | -0.2228396 | 13000 and 0.36 |
| Quantity adjustment | 18223.0 | 5.4754876 | 13000 and 0.36 |
| Vertical monopoly | 804.5 | -95.3435203 | 13400 and 0.26 |
| Vertical monopoly | 2143.5 | -87.5933322 | 13400 and 0.26 |
| Vertical monopoly | 17279.0 | 0.0115761 | 13400 and 0.26 |
| Price setting | 17240.5 | -0.2112635 | 13400 and 0.26 |
| Quantity adjustment | 18224.0 | 5.4812757 | 13400 and 0.26 |
| Vertical monopoly | 696.0 | -95.9715228 | 13800 and 0.15 |
| Vertical monopoly | 2251.0 | -86.9711177 | 13800 and 0.15 |
| Vertical monopoly | 17279.5 | 0.0144701 | 13800 and 0.15 |
| Price setting | 17242.0 | -0.2025815 | 13800 and 0.15 |
| Quantity adjustment | 18225.5 | 5.4899577 | 13800 and 0.15 |
| Vertical monopoly | 601.0 | -96.5213868 | 14200 and 0.05 |
| Vertical monopoly | 2345.5 | -86.4241477 | 14200 and 0.05 |
| Vertical monopoly | 17280.5 | 0.0202581 | 14200 and 0.05 |
| Price setting | 17244.0 | -0.1910054 | 14200 and 0.05 |
| Quantity adjustment | 18226.5 | 5.4957458 | 14200 and 0.05 |
| Price setting | 17251.0 | -0.1504891 | 12100 and 0.88 |
| Vertical monopoly | 17282.5 | 0.0318342 | 12100 and 0.88 |
| Quantity adjustment | 18224.0 | 5.4812757 | 12100 and 0.88 |
| Price setting | 17253.5 | -0.1360190 | 12540 and 0.78 |
| Vertical monopoly | 17283.5 | 0.0376223 | 12540 and 0.78 |
| Quantity adjustment | 18225.5 | 5.4899577 | 12540 and 0.78 |
| Price setting | 17256.0 | -0.1215489 | 12980 and 0.67 |
| Vertical monopoly | 17284.0 | 0.0405163 | 12980 and 0.67 |
| Quantity adjustment | 18227.0 | 5.4986398 | 12980 and 0.67 |
| Price setting | 17258.5 | -0.1070788 | 13420 and 0.57 |
| Vertical monopoly | 17285.0 | 0.0463043 | 13420 and 0.57 |
| Quantity adjustment | 18228.5 | 5.5073219 | 13420 and 0.57 |
| Vertical monopoly | 1384.0 | -91.9893500 | 13860 and 0.47 |
| Vertical monopoly | 1557.0 | -90.9880188 | 13860 and 0.47 |
| Vertical monopoly | 17286.0 | 0.0520924 | 13860 and 0.47 |
| Price setting | 17261.5 | -0.0897146 | 13860 and 0.47 |
| Quantity adjustment | 18230.0 | 5.5160039 | 13860 and 0.47 |
| Vertical monopoly | 1070.5 | -93.8039011 | 14300 and 0.36 |
| Vertical monopoly | 1869.5 | -89.1792557 | 14300 and 0.36 |
| Vertical monopoly | 17287.0 | 0.0578804 | 14300 and 0.36 |
| Price setting | 17264.0 | -0.0752445 | 14300 and 0.36 |
| Quantity adjustment | 18231.5 | 5.5246860 | 14300 and 0.36 |
| Vertical monopoly | 911.0 | -94.7270938 | 14740 and 0.26 |
| Vertical monopoly | 2028.0 | -88.2618510 | 14740 and 0.26 |
| Vertical monopoly | 17287.5 | 0.0607744 | 14740 and 0.26 |
| Price setting | 17266.5 | -0.0607744 | 14740 and 0.26 |
| Quantity adjustment | 18233.0 | 5.5333681 | 14740 and 0.26 |
| Vertical monopoly | 788.0 | -95.4390230 | 15180 and 0.15 |
| Vertical monopoly | 2150.5 | -87.5528159 | 15180 and 0.15 |
| Vertical monopoly | 17288.5 | 0.0665625 | 15180 and 0.15 |
| Price setting | 17269.0 | -0.0463043 | 15180 and 0.15 |
| Quantity adjustment | 18234.5 | 5.5420501 | 15180 and 0.15 |
| Vertical monopoly | 683.5 | -96.0438734 | 15620 and 0.05 |
| Vertical monopoly | 2254.0 | -86.9537535 | 15620 and 0.05 |
| Vertical monopoly | 17289.5 | 0.0723505 | 15620 and 0.05 |
| Price setting | 17272.0 | -0.0289402 | 15620 and 0.05 |
| Quantity adjustment | 18236.0 | 5.5507322 | 15620 and 0.05 |
## Saving 7 x 5 in image
## # A tibble: 3 × 24
## X identifier names names_2 x values lag_sign Stable beta alpha
## <int> <int> <chr> <chr> <dbl> <dbl> <int> <chr> <dbl> <dbl>
## 1 555 145 Price set… ss_ber… 17310. 0.0653 2 Stable 1564. 1.63e6
## 2 558 146 Price set… ss_ber… 17294. 0.0192 2 Stable 1564. 1.63e6
## 3 560 147 Price set… ss_ber… 17277 0.0513 2 Stable 1564. 1.63e6
## # ℹ 14 more variables: gamma <dbl>, W <dbl>, W1 <dbl>, W2 <dbl>, c <int>,
## # v <dbl>, r <dbl>, k <int>, interest_rate <dbl>, sigma <dbl>, spec <chr>,
## # transformation <dbl>, id_2 <int>, x_norm <dbl>
## # A tibble: 6 × 6
## identifier names x alpha gamma3 Stable
## <int> <chr> <dbl> <fct> <fct> <chr>
## 1 1869 Quantity adjustment 763 1.8 50% Stable
## 2 1869 Quantity adjustment 3578. 1.8 50% Unstable
## 3 1869 Quantity adjustment 15886. 1.8 50% Stable
## 4 1869 Price setting 909 1.8 50% Stable
## 5 1869 Price setting 4996. 1.8 50% Unstable
## 6 1869 Price setting 14322. 1.8 50% Stable
## Saving 7 x 5 in image
## Figure (SM) and 1 in Main : Alternative with extinction -
Hypothetical schematic of equilibrium points under different poaching
harvest functions
## Saving 7 x 5 in image
Define :
q_(x, N, M, ...) : Cournot harvest with
N traders and M farmers (in metric
tons)
cournot_harvest(x, ...) : Cournot harvest with 1
trader and 1 farmer (in metric tons)
monop_harvest(x, ...): Monopoly harvest (in metric
tons)
growth(x, ...) : logistic growth function, yields
growth of population (in metric tons)
## # A tibble: 15 × 2
## x names
## <int> <chr>
## 1 884 ss_5players
## 2 968 ss_2players
## 3 969 ss_2players
## 4 3264 ss_2players
## 5 3265 ss_2players
## 6 4974 ss_5players
## 7 4975 ss_5players
## 8 14366 ss_5players
## 9 14367 ss_5players
## 10 14368 ss_5players
## 11 15993 ss_2players
## 12 17234 ss_price
## 13 17235 ss_price
## 14 17277 ss_monop
## 15 17680 ss_quantity
## Market configuration Low stable steady state Middle unstable steady state
## 1 5 players 884 4975
## 2 2 players 969 3265
## 3 Vertical monopoly <NA> <NA>
## 4 Price setting <NA> <NA>
## 5 Quantity adjustment <NA> <NA>
## High stable steady state
## 1 14366
## 2 15993
## 3 17277
## 4 17235
## 5 17680
In this section, we investigate the effect of a ‘vertical monopoly’ take over the aquaculture facility. See supplementary materials section ??? for derivation and discussions.
Identify values :
## Monopoly Takeover_ Cournot_
## 1 17277 6.572322 5.458124
Finally, identify bioeconomic performance :
| Scenario | Harvest in (mt) | Stock in (mt) | Price paid to poachers (USD/mt) | Profit in 10^6 USD |
|---|---|---|---|---|
| Vertical Monopoly | 507.0368 | 17277.0 | 40074.45 | 402.0208 |
| Cournot Competition | 363.7271 | 18220.0 | 36538.33 | 206.8650 |
| Cartel takeover | 332.2972 | 18412.5 | 35861.28 | 419.9162 |
First, we calibrate a hypothetical cost of transaction based on most recent observed price data. Assume that the cost of transaction is 100% of the observed price paid to poachers in most recent data.
The observed price per kilogram of totoaba in most recent years is 483.0116732 USD. The model is expressed in metric tons, so we use the metric ton numbers instead to parameterize an idea of the worst case trading costs.
## [1] 289807
Need to evaluate economic performance
## [,1] [,2]
## [1,] "Structure" "Steady state"
## [2,] "Profit of monopoly with large costs (in million)" "17895"
## [3,] "Profit of quantity setting (in million)" "18220"
## [4,] "Profit of price setting (in million)" "17234.5"
## [,3] [,4] [,5] [,6]
## [1,] "Variation in %" "Poaching" "Variation in %" "Profit"
## [2,] " " "415.12" " " "189.51"
## [3,] "1.82" "363.73" "-12.38" "206.87"
## [4,] "-3.69" "513.08" "23.6" "87.71"
## ss_monop_large ss_monop_low ss_bertrand_val ss_cournot
## 1 17895 17277 17234.5 18220
## ss_bertrand_share_large ss_cournot_share_large poaching_monop_large
## 1 -3.690975 1.81615 415.1169
## poaching_bertrand poaching_cournot poaching_cournot_rel poaching_bertrand_rel
## 1 513.0788 363.7271 -12.37958 23.59865